_Higher Mathematics for Students of Chemistry and Physics (London, 1902), Prologue._ =1913.= The calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word. --OSGOOD, W. F. _Bulletin American Mathematical Society, Vol. 13 (1907), p. 467._ =1914.= [Infinitesimal] analysis is the most powerful weapon of thought yet devised by the wit of man.--SMITH, W. B. _Infinitesimal Analysis (New York, 1898), Preface, p. vii._ =1915.= The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature. And, as it is that which hath enabled them so remarkably to outgo the ancients in discovering theorems and solving problems, the exercise and application thereof is become the main if not sole employment of all those who in this age pass for profound geometers.--BERKELEY, GEORGE. _The Analyst, sect. 3._ =1916.= I have at last become fully satisfied that the language and idea of infinitesimals should be used in the most elementary instruction--under all safeguards of course.--DE MORGAN, A. _Graves’ Life of W. R. Hamilton (New York, 1882-1889), Vol. 3, p. 479._ =1917.= Pupils should be taught how to differentiate and how to integrate simple algebraic expressions before we attempt to teach them geometry and these other complicated things. The dreadful fear of the symbols is entirely broken down in those cases where at the beginning the teaching of the calculus is adopted. Then after the pupil has mastered those symbols you may begin geometry or anything you please. I would also abolish out of the school that thing called geometrical conics. There is a great deal of superstition about conic sections. The student should be taught the symbols of the calculus and the simplest use of these symbols at the earliest age, instead of these being left over until he has gone to the College or University. --THOMPSON, S. P. _Perry’s Teaching of Mathematics (London, 1902), p. 49._ =1918.= Every one versed in the matter will agree that even the elements of a scientific study of nature can be understood only by those who have a knowledge of at least the elements of the differential and integral calculus, as well as of analytical geometry--i.e. the so-called lower part of the higher mathematics.... We should raise the question, whether sufficient time could not be reserved in the curricula of at least the science high schools [Realanstalten] to make room for these subjects....